Perhaps the most amazing thing I've read on the failure of one's consciousness to continue was in Part III of Derek Parfit's Reasons and Persons, which is concerned with the question of personal identity: What makes it the case that I'm the same person from one time to another?
Parfit argues for a reductionist view of personal identity on which my being the same person from moment to moment is just a matter of various chains of psychological connectedness holding between my earlier and later self. For example, there are chains of memory and intention going from that connect me now to myself when I was five years old. That's what makes me the same person across time. While I may now differ significantly from my five-year-old self, I'm connected to him by a set of smooth day-to-day psychological transitions. Parfit rejects the non-reductionist view that most of us seem to hold, on which my being the same person now and then is a matter of some further, significant, sui generis fact. He explains how seeing this changed his attitude towards death:
